Bayes Shrinkage Estimators of Weibull Parameters

Shrinking an unbiased estimator of a parameter towards a prior value of the parameter has been treated by Thompson, Lemmer, and others. The shrunken estimator is better than the unbiased estimator if true value of the parameter is close to its prior value and is less s-efficient otherwise. This paper considers whether it would be more realistic to postulate a prior distribution for the 2-parameters of the Weibull distribution around the prior values and use ordinary Bayes estimators instead of prior values in the shrunken estimator. Bayes shrinkage estimators have been obtained and their s-efficiencies were studied via Monte Carlo. The Bayes shrinkage estimators are better than the unbiased estimators.